Benacerraf P., Putnam H. (eds.) Philosophy of Mathematics: Selected Readings

Second Edition. — Cambridge; New York: Cambridge University Press, 1983. — 600 p. — ISBN: 0-521-22796-8.The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.Symposium on the foundations of mathematics
1. The logicist foundations of mathematics / Rudolf Carnap
2. The intuitionist foundations of mathematics / Arend Heyting
3. The formalist foundations of mathematics / Johann Von Neumann
Disputation / Arend Heyting
Intuitionism and formalism / L.E.J. Brouwer
Consciousness, philosophy, and mathematics / L.E.J. Brouwer
The philosophical basis of intuitionistic logic / Michael Dummett
The concept of number / Gottlob Frege
Selections from Introduction to mathematical philosophy / Bertrand Russell
On the infinite / David Hilbert
Remarks on the definition and nature of mathematics / Haskell B. Curry
Hilbert's programme / Georg Kreisel
Empiricism, semantics, and ontology / Rudolf Carnap
On platonism in mathematics / Paul Bernays
What numbers could not be / Paul Benacerraf
Mathematics without foundations / Hilary Putnam
The a priori / Alfred Jules Ayer
Truth by convention / W.V. Quine
Carnap and logical truth / W.V. Quine
On the nature of mathematical reasoning / Henri Poincare
Mathematical truth / Paul Benacerraf
Models and reality / Hilary Putnam
Russell's mathematical logic / Kurt Gödel
What is Cantor's continuum problem? / Kurt Gödel
The iterative concept of set / George Boolos
What is the iterative conception of set? / Charles Parsons
The concept of set / Hao Wang